Most class trials cannot do much, ie. not enter any dungeon / raid.
So they must not be shown in the list.

Just delete them?

Not sure if I can follow you. Do you mean delete the characters off the WoW servers or from the AddOn ?
If the latter, I did not know you could do that. But, the problem still exists on newely created class trial characters then.

Well both, you can ignore as many chars as you want

Can this not be automated? (AddOn checks if logged in character is a non class trial character)